Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets

A theory of exceptional extreme events, characterized by their abnormal sizes compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns, city-size distributions (e.g., Paris in France and London in the UK), in material failure, epileptic seizure intensities, and other systems. Within our theory, the large outliers are interpreted as droplets of Bose-Einstein condensate: the appearance of outliers is a natural consequence of the occurrence of Bose-Einstein condensation controlled by the relative degree of attraction, or utility, of the largest entities. For large populations, Zipf's law is recovered (except for the dragon-king outliers). The theory thus provides a parsimonious description of the possible coexistence of a power law distribution of event sizes (Zipf's law) and dragon-king outliers.Comment: Latex file, 16 pages, 1 figur

Habitat utilization by coral reef fish: implications for specialists vs. generalists in a changing environment

The impact of environmental disturbance and habitat loss on associated species is expected to be dependent on a species' level of specialization. We examined habitat use and specialization of coral reef fish from the diverse and ecologically important family Pomacentridae, and determined which species are susceptible to declines in coral cover due to disturbance induced by crown-of-thorns seastar (COTS, Acanthaster planci L.). A high proportion of pomacentrid species live in association with live coral as adults (40%) or juveniles (53%). Adults of many species had strong affiliations with branching corals, while juveniles favoured plating growth forms, reflecting the sizes of refuge provided by coral types. Juveniles of species that associated with coral had narrower niche breadths than adult conspecifics, due to associations with specific coral types. The especially high coral association and narrower niche breadth of juveniles suggest that the presence of live coral is crucial for many species during early life history, and that disturbance-induced coral loss may have serious flow-on effects on adult abundance. Microhabitat availability was a poor predictor of fish species abundance. Significant correlations between coverage of coral types and abundance of five adults and two juvenile species were detected; however, these relationships explaine